In mathematical parlance, a random walk is a random process consisting of a sequence of discrete steps of fixed length. As far as it applies to this blog, a random walk is an anything-and-everything forum for what's on my mind, covering philosophy, science, religion, world events, and anything else in my purview.
The long, twisted marathon that was the 2008 presidential campaign is now over, and Barack Obama has been elected our next president. I am writing this with a profound sense of relief at the outcome, and I am heartened by the reaction of people around the world.
In one day, the United States has earned a tremendous amount of worldwide goodwill ... and it didn't even take a tragedy for us to get it. I am confident that President Obama will be a better steward of that benevolence and that America will once again be seen as a beacon of hope around the world, not the font of disappointment it has recently been.
Mr. Obama's opponents frequently criticized the messiah-like treatment he was receiving, so one would be wise to use caution in lavishing praise on our new president before he has even taken office. Instead I will praise the tens of millions of Americans who used this election to vote their hopes instead of their fears. And for those whose votes went the other way, I urge you to stay tuned and give the new president a chance. You might be pleasantly surprised.
You already know she is a young-Earth creationist. You already know that she is expecting the return of Jesus in her lifetime. But maybe you don't yet know why she is the best candidate to lead the country through the "end times." In the video below, you'll learn that Alaska will be a "refuge for the lower 48," and that Sarah's friends in Wasilla are prepared for the monumental task of ministering to those at risk of being on the wrong end of God's almighty smite stick.
There are several things worth noting in the video. First, a commercial for the religious group Palin is supporting (the video begins with her speaking at the group's "graduation" ceremony) is cut into the middle of the video to provide some context. This group, in Palin's hometown of Wasilla, is convinced that the end of the world is near. One of the crucial things to notice is the choice of graphics employed in the commercial. There is a very strong indication that this group believes nuclear war to be the thing to usher in the end of the world. Of course, a nuclear war would usher in the end of the world, at least as we know it. The difference is that this group believes that it will also herald the return of Jesus.
Under no circumstances should a person who considers such a calamity both positive and inevitable (in her lifetime) be allowed to have control over a nuclear arsenal. Sarah Palin stands an extraordinarily good chance of assuming the presidency if John McCain is elected. She has also casually indicated that it might be worthwhile to go to war with Russia for the sake of Georgia, a place she certainly knows next to nothing about.
Zealots have been forecasting the "imminent" end of the world for centuries, and they have always gotten it wrong. But fundamentalist Christians finally have a chance to make half of their dream come true. They now have a candidate in position who could soon have the power to end all of human civilization in the span of a single afternoon.
Were such a disaster to happen, only a suffering few among the credulous who actively sought to bring about man's last days would spend the agonizing wait for a savior who would never come, while the dead would never know how wrong they were.
You may have seen one of several news reports in the past few years that reported on surveys of the sexual behavior of Americans. In particular, you may have seen lines such as this one: “Overall, women report an average of six sex partners in their lifetimes, men, 20.”1 Now, if you’re a woman, maybe you read this and thought to yourself, “Boy, men sure are dogs. No wonder they can’t seem to commit to a relationship. They’re always off trying to find something to rub up against!” And if you’re a man, perhaps you thought that you have really underperformed relative to your fellow men.
But did you stop to question the validity of the numbers? Maybe you leafed through the full survey results. There are colorful graphs and some statistical terminology. The conclusions must be legitimate, right? Not even close.
Perhaps it did occur to you that it seems strange for the average number of sexual partners for men to be so much larger than that for women. Shouldn’t they be closer together? (Yes.) Should they be the same? (Not necessarily.)
Why are the statistics so different? Well, people lie, especially about sex.To motivate our discussion a bit, let’s have a look at the chart below (click on it to see a larger version).
This is a matrix, of sorts, representing a hypothetical population of 20 men and 21 women. The sexual relationships among those in the group are indicated by whether there is a numeral one in the cell that lies at the intersection of a row representing a male and a column representing a woman. For instance, we see that male number 11 and female number 12 have gotten it on with each other, whereas male 14 and female 14 have not known each other in the biblical sense. Notice also that male number 12 is a virgin.
Male number 10 is the stud in the group. We can see a lot of ones in his row, and we can see from the sum in the far-right column that male number 10 has slept with more than half of the women in the population (over 57 percent, in fact).
You probably know how to compute an arithmetic average, which is just the sum of all the numbers on a list divided by the total number of items on that list. To find the average number of partners for the men, we add the numbers in the right-most column, which gives us the total number of sexual relationships for all of the men.2 The average number of partners among the men is 3.0. We use the same idea to compute the average for the women, this time adding up the numbers in the bottom row and dividing by the total number of women. The average number of partners among women is about 2.86.
Notice that the sum of the relationships for the men is the same as the sum of the relationships for the women, namely 60. This is necessarily so. After all, we can count up all of the ones on our table either row by row or column by column. Either way, we should get the same answer. It also makes intuitive sense, since for a man to have a sexual relationship with a woman, it is required that a woman have a sexual relationship with a man!
This is going to be the case in any complete population under consideration: The total number of relationships will be the same for both the men and the women. The average can be a little different, however, because it is not necessarily the case that there are exactly as many men as there are women. I haven’t looked it up, but for the purposes of the rest of this document, let us say that there are 51 percent women and 49 percent men in the American population. I think that is actually pretty close to being true.
We can represent the proportion of men in the population by the letter p (where p = 0.49). Necessarily, then, the proportion of women in the population is given by 1 - p. If the total population is the sum of the men and women, given by , then and .
As we showed earlier, the sum of sexual relationships is the same for both the men and the women. Let us represent this number by S. The average number of partners for men is therefore given by , and the average number of partners for women is given by .
We will assume that the average is higher for men (which it should be if there are fewer men in the population). We can represent the difference of the averages by
But recall from above that , so we can write
We see, then, that the difference between the averages is a function of the average for the men and the proportion of the population made up by men. If the 49 percent figure I mentioned above is correct, then it should be the case that . At any rate, the difference between the averages cannot be greater than four percent of the average for the men, a pretty trivial amount. The difference shrinks further the closer the men and women get to a 50-50 split in the population. In our model, if the men are telling the truth, the average number of sexual partners for women should be 19.2, not six.
But the men are probably lying. Many probably overstated their sexual histories, bumping the average up. The women are probably also lying by understating their sexual histories to avoid coming off as tramps.3
We are left feeling disappointed in this survey, which was apparently never vetted by a competent statistician. It appears that, for now, the truth about Americans’ sex lives will stay between the sheets.
1. From the ABC News Primetime Live Poll: The American Sex Survey, October 21, 2004.
2. Here I refer to “sexual relationships” rather than “partners” in order to avoid confusion, since some women will be counted more than once if they slept with different men.
3. The other possibility is that these numbers are correct but that participants were drawn from wildly different populations: relatively normal women and bar-hopping studs. This is a possibility, but it is remarkably improbable. [Note: A PDF version of this article can be found here.]
Below are excerpts from a September 3, 2008, entry on the blog Progressive Alaska. In it, blogger Philip Munger details the few informal meetings he had with the woman who would become the current Republican vice-presidential nominee, Sarah Palin. The key issue raised in the piece—and the thing that frightens me most about her—is that she is apparently among those who regard the end of the world as a good thing. Considering how easily that can be helped along by Republican hawks with a nuclear (let the spelling guide your pronunciation, Sarah) arsenal, these beliefs are anything but innocuous, and they certainly do not suggest to me any firmer moral foundation than what is possessed by a rationalist nonbeliever who does not require the threat of damnation to motivate his good works. More after the excerpt.
I first met Alaska Governor and GOP Vice Presidential aspirant Sarah Palin when she was on the City of Wasilla Planning Commission. ... Of the encounters I've since had with Sarah Palin, two that brought up her faith, have become important, in light of the possibility that she might someday soon be in charge of thousands of thermonuclear weapons.
In June 1997, both Palin and I had responsibilities at the graduation ceremony of a small group of Wasilla area home schoolers. ... Palin had recently become Wasilla mayor, beating her earliest mentor, John Stein, the then-incumbent mayor. A large part of her campaign had been to enlist fundamentalist Christian groups, and invoke evangelical buzzwords into her talks and literature.
As the ceremony concluded, I bumped into her in a hall away from other people. I congratulated her on her victory, and took her aside to ask about her faith. Among other things, she declared that she was a young earth creationist, accepting both that the world was about 6,000-plus years old, and that humans and dinosaurs walked the earth at the same time.
I asked how she felt about the second coming and the end times. She responded that she fully believed that the signs of Jesus returning soon "during MY lifetime," were obvious. "I can see that, maybe you can't - but it guides me every day."
Our next discussion about religion was after she had switched to the less strict Wasilla Bible Church. ... Once again, we found ourselves being able to talk privately. I reminded her of the earlier conversation, asking her if her views had changed. She was no longer "necessarily" a young earth creationist, she told me. But she strongly reiterated her belief that "The Lord is coming soon." I was trying to get her to tell me what she felt the signs were, when she had to move on.
Let me take a moment to say something about young-Earth creationism, just in case anyone believes it to be a defensible alternative to the scientific view. If it were true that Earth is on the order of 6,000 years old, it would mean that our basic understanding of fundamental physics is mistaken. The casual reader may not see a problem with that. But one of the ways that science shows that it is working is by having its facts confirmed over and over again, often by different methods being applied in different fields by researchers looking into very different things. When it comes to the age of Earth, there isn't just one way of getting the answer. Numerous, fundamentally different ways of estimating Earth's age are possible, and all of those methods agree on the answer. The take-home lesson is that they agree on the answer—that Earth is roughly 4.5 billion years old—because the answer is probably pretty accurate.
These methods are based on a web of knowledge that forms our current scientific understanding. And, put simply, if we are wrong about the planet's age, then we are also wrong about most of physics. Your very ability to read this sentence on your computer depends on technology whose theoretical basis is the same system of physical principles responsible for the various methods of finding the age of Earth. The upshot is that our technology—and that includes your computer—would simply not work if our understanding of these fundamental ideas were so flawed. The ideas are so interwoven, in fact, that you cannot simply say that perhaps only our understanding of the physics behind the age of Earth is flawed. It doesn't work that way. The preponderance of the evidence, which includes your day-to-day experience with technology, shows that the young-Earth story is pure fiction.
Back on the topic of Sarah Palin, I could say more, but I think Matt Damon sums it up pretty well in this video clip:
"In the Bullshit Department, a businessman can't hold a candle to a clergyman. 'Cause I gotta tell you the truth, folks: When it comes to bullshit—big-time, major-league bullshit—you have to stand in awe of the all-time champion of false promises and exaggerated claims: religion. No contest. No contest. Religion.
"Religion easily has the greatest bullshit story ever told. Think about it. Religion has actually convinced people that there's an invisible man—living in the sky—who watches everything you do, every minute of every day. And the invisible man has a special list of ten things he does not want you to do. And if you do any of these ten things, he has a special place, full of fire and smoke and burning and torture and anguish, where he will send you to live and suffer and burn and choke and scream and cry forever and ever 'til the end of time! But he loves you.
"He loves you, and he needs money! He always needs money! He's all-powerful, all-perfect, all-knowing, and all-wise; somehow ... just can't handle money! Religion takes in billions of dollars, they pay no taxes, and they always need a little more. Now, you talk about a good bullshit story. Holy shit!"
I have never been content doing just one thing. Even my favorite things in life—chiefly music, science, and literature—could not sustain my interest if they made up my entire day. In one way or another, I am a perpetual student, and I am always excited by the opportunity to learn something new.
